From Wikipedia, the free encyclopedia

The ancient Egyptian units of measurement are those used by the dynasties of ancient Egypt prior to its incorporation in the Roman Empire and general adoption of Roman, Greek, and Byzantine units of measurement. The units of length seem to have originally been anthropic, based on various parts of the human body, although these were standardized using cubit rods, strands of rope, and official measures maintained at some temples.

Following Alexander the Great's conquest of Persia and subsequent death, his bodyguard and successor Ptolemy assumed control in Egypt, partially reforming its measurements, introducing some new units and hellenized names for others.

Length

Egyptian units of length are attested from the Early Dynastic Period. Although it dates to the 5th dynasty, the Palermo stone recorded the level of the Nile River during the reign of the Early Dynastic pharaoh Djer, when the height of the Nile was recorded as 6 cubits and 1 palm [1] (about 3.217 m or 10 ft 6.7 in). A Third Dynasty diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon depicting this diagram was found near the Step Pyramid of Saqqara. A curve is divided into five sections and the height of the curve is given in cubits, palms, and digits in each of the sections. [2] [3]

At some point, lengths were standardized by cubit rods. Examples have been found in the tombs of officials, noting lengths up to remen. Royal cubits were used for land measures such as roads and fields. Fourteen rods, including one double-cubit rod, were described and compared by Lepsius. [4] Two examples are known from the Saqqara tomb of Maya, the treasurer of Tutankhamun. Another was found in the tomb of Kha ( TT8) in Thebes. These cubits are about 52.5 cm (20.7 in) long and are divided into palms and hands: each palm is divided into four fingers from left to right and the fingers are further subdivided into ro from right to left. The rules are also divided into hands [5] so that for example one foot is given as three hands and fifteen fingers and also as four palms and sixteen fingers. [6] [3] [7] [8] [9] [5]

Cubit rod from the Turin Museum.

Surveying and itinerant measurement were undertaken using rods, poles, and knotted cords of rope. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots tied at regular intervals. Similar scenes can be found in the tombs of Amenhotep-Sesi, Khaemhat and Djeserkareseneb. The balls of rope are also shown in New Kingdom statues of officials such as Senenmut, Amenemhet-Surer, and Penanhor. [2]

Units of Length [6] [2]
Names Equivalents
English Egyptian Coptic Palms Digits Metric [10]
Digit [11]
Finger [12]
Fingerbreadth [11]
Tebā [13]
D50
[a]
ḏb ⲧⲏⲏⲃⲉ [15] [16] tēēbe 14 1 1.875 cm
Palm [11]
Hand [17]
Shesep [18]
D48
[b]
šsp ϣⲟⲡ [19] [16]
ϣⲟⲟⲡ [19]
ϣⲱⲡ [19]
ϣⲁⲡ [19]
shop
shoop
shōp
shap
1 4 7.5 cm
Hand [20]
Handsbreadth [18]
D46
[c]
ḏrt ϩⲱϩϥ [21] [22] hōhf 1+14 5 9.38 cm
Fist [18]
D49
[d]
ḫf [18]
ꜣmm [14]
ϭⲁϫⲙⲏ [23]
ϫⲁⲙⲏ [23]
qajmē
jamē
1+12 6 11.25 cm
Double Handbreadth [14]
D48
D48
[e]
šspwy 2 8 15 cm [14]
Small Span [18]
Pedj-Sheser
Shat Nedjes [18]
Little Shat [12]
H7G37
p šsr
š ꜣt n ḏs [18]
ⲣⲧⲱ [24] [22]
ⲉⲣⲧⲱ [25]
rtō
ertō
3 12 22.5 cm
Great Span [18]
Half-Cubit [14]
Pedj-Aa
Shat Aa [18]
Great Shat [12]
H7O29
[f]
pḏ [18] [14]
š ꜣt [18]
3+12 14 26 cm
Foot
Djeser [18]
Ser [13]
Bent Arm [18]
D45
ḏsr 4 16 30 cm
Shoulder
Remen [18]
Upper Arm [18]
D41
rmn 5 20 37.5 cm
Small Cubit [20]
Short Cubit [18]
Meh Nedjes [18]
D42G37
m n ḏs
m šsr
ⲙⲁϩⲉ [26] [16]
ⲙⲉϩⲓ [27]
mahe
mehi
6 24 45 cm
Cubit
Royal Cubit [18]
Sacred Cubit [17]
Meh Nesut [11]
Meh Nisut [18]
Mahi
Ell [26]
D42
[g]
m 7 28 52.3 cm [11]
52.5 cm [17]
Pole
Nebiu [28]
N35
D58
M17V1T19
nbiw 8 32 60 cm
Rod
Rod of Cord
Stick of Rope [20]
Khet [11]
Schoinion [29]
W24G43V28
[h]
ḫt ϩⲱⲧⲉ [31]
ϩⲱϯ [31]
hōte
hōti
100 cubits [11] 52.5 m [29]
Schoenus [14]
River-Measure
League [14]
Ater [11]
Iter [20] or Iteru [14]
M17X1
D21
G43N35BN36
N21 Z1
[i]
i͗trw ϣϥⲱ [32]
ϣⲃⲱ [32]
shfō
shvō
20,000 cubits [11] 10.5 km [11]

The digit was also subdivided into smaller fractions of 12, 13, 14, and 116. [33] Minor units include the Middle Kingdom reed of 2 royal cubits, [j] the Ptolemaic xylon ( Greek: ξύλον, lit. "timber") of three royal cubits, [34] [35] the Ptolemaic fathom ( Greek: ὀργυιά, orgyiá; Ancient Egyptian: ḥpt; Coptic: ϩⲡⲟⲧ, hpot) of four lesser cubits, [36] and the kalamos of six royal cubits. [17]

Area

Records of land area also date to the Early Dynastic Period. The Palermo stone records grants of land expressed in terms of kha and setat. Mathematical papyri also include units of land area in their problems. For example, several problems in the Moscow Mathematical Papyrus give the area of rectangular plots of land in terms of setat and the ratio of the sides and then require the scribe to solve for their exact lengths. [6]

The setat was the basic unit of land measure and may originally have varied in size across Egypt's nomes. [20] Later, it was equal to one square khet, where a khet measured 100 cubits. The setat could be divided into strips one khet long and ten cubit wide (a kha). [2] [6] [37]

During the Old Kingdom:

Units of Area
Names Equivalents [38]
English Egyptian Coptic Setat Square
Cubits
Metric
Sa [20]
Eighth
G39
z 1800 12+12 3.4456 m2
Heseb
Fourth
Account Unit [20]
Z9
ḥsb 1400 25 6.8913 m2
Remen
Half
Shoulder [20]
D41
rmn 1200 50 13.783 m2
Ta
Khet [38]
Cubit [39]
Cubit of Land [39]
Land Cubit [14]
Ground Cubit [39]
Cubit Strip [39]
Land Unit [20]
N17
[k]
t
ḫt
m
m itn
ϫⲓⲥⲉ [40] [22] jise 1100 100 [38] 27.565 m2
Kha
Thousand [20]
M12
110 1,000 275.65 m2
Setat [38]
Setjat [38]
Aroura [38]
Square Khet [38]
stF29t
Z4
[l]
s [29]
s ꜣt [38]
ⲥⲱⲧ [41] [22]
ⲥⲧⲉⲓⲱϩⲉ [42] [22]
sōt
steiōhe
1 10,000 2,756.5 m2

During the Middle and New Kingdom, the "eighth", "fourth", "half", and "thousand" units were taken to refer to the setat rather than the cubit strip:

Sa
Eighth
G39
[m]
s 18 1,250 345 m2
Heseb
Fourth
Z9
[n]
hsb
r-fdw
14 2,500 689 m2
Gs
Remen
Half
Aa13
[o]
gs ⲣⲉⲣⲙⲏ [22] rermē 12 5,000 1378 m2
Kha
Thousand
M12
[p]

t
10 100,000 2.76 ha

During the Ptolemaic period, the cubit strip square was surveyed using a length of 96 cubits rather than 100, although the aroura was still figured to compose 2,756.25 m2. [17] A 36 square cubit area was known as a kalamos and a 144 square cubit area as a hamma. [17] The uncommon bikos may have been 1+12 hammata or another name for the cubit strip. [17] The Coptic shipa (ϣⲓⲡⲁ) was a land unit of uncertain value, possibly derived from Nubia. [43]

Volume

A bronze capacity measure inscribed with the cartouches of the birth and throne names of Amenhotep III of the 18th Dynasty

Units of volume appear in the mathematical papyri. For example, computing the volume of a circular granary in RMP 42 involves cubic cubits, khar, heqats, and quadruple heqats. [6] [9] RMP 80 divides heqats of grain into smaller henu.

Problem 80 on the Rhind Mathematical Papyrus: As for vessels (debeh) used in measuring grain by the functionaries of the granary: done into henu, 1 hekat makes 10; 12 makes 5; 14 makes 2+12; etc. [6] [9]
Units of Volume [6] [2]
Names Equivalents
English Egyptian Heqats Ro Metric
Ro
r
r 1320 1 0.015 L
Dja dja 116 20 [44] 0.30 L
Jar
Hinu
hn
W24 V1
W22
hnw 110 32 0.48 L
Barrel
Heqat
Hekat
U9
hqt 1 320 4.8 L
Double Barrel
Double Heqat
Double Hekat
hqty 2 640 9.6 L
Quadruple Heqat ( MK) [45]
Oipe [46] ( NK) [45]
T14U9

ip
t
U9
hqt-fdw
jpt [20]
ipt [45]
4 1,280 19.2 L
Sack
Khar
Aa1
r
khar 20 ( MK)
16 ( NK) [47]
6,400 ( MK)
5120 ( NK)
96.5 L ( MK)
76.8 L ( NK) [47]
Deny
Cubic cubit
deny 30 9,600 144 L

The oipe was also formerly romanized as the apet. [48]

Weight

Green glazed faience weight discovered at Abydos, inscribed for the high steward Aabeni during the late Middle Kingdom
Serpentine weight of 10 daric, inscribed for Taharqa during the 25th Dynasty

Weights were measured in terms of deben. This unit would have been equivalent to 13.6 grams in the Old Kingdom and Middle Kingdom. During the New Kingdom however it was equivalent to 91 grams. For smaller amounts the qedet (110 of a deben) and the shematy (112 of a deben) were used. [2] [9]

Units of Weight [2]
Names Equivalents
English Egyptian Debens Metric
Piece
Shematy
shȝts 112
Qedet
Kedet
Kite
Aa28X1
S106
qdt 110
Deben
D46D58N35
F46
dbn 1 13.6 g ( OK & MK)
91 g ( NK)

The qedet or kedet is also often known as the kite, from the Coptic form of the same name (ⲕⲓⲧⲉ or ⲕⲓϯ). [49] In 19th-century sources, the deben and qedet are often mistakenly transliterated as the uten and kat respectively, although this was corrected by the 20th century. [50]

Time

The former annual flooding of the Nile organized prehistoric and ancient Egypt into three seasons: Akhet ("Flood"), Peret ("Growth"), and Shemu or Shomu ("Low Water" or "Harvest"). [51] [52] [53]

The Egyptian civil calendar in place by Dynasty V [54] followed regnal eras resetting with the ascension of each new pharaoh. [55] It was based on the solar year and apparently initiated during a heliacal rising of Sirius following a recognition of its rough correlation with the onset of the Nile flood. [56] It followed none of these consistently, however. Its year was divided into 3 seasons, 12 months, 36 decans, or 360 days with another 5 epagomenal days [57]—celebrated as the birthdays of five major gods [58] but feared for their ill luck [59]—added "upon the year". The Egyptian months were originally simply numbered within each season [60] but, in later sources, they acquired names from the year's major festivals [61] and the three decans of each one were distinguished as "first", "middle", and "last". [62] It has been suggested that during the Nineteenth Dynasty and the Twentieth Dynasty the last two days of each decan were usually treated as a kind of weekend for the royal craftsmen, with royal artisans free from work. [63] This scheme lacked any provision for leap year intercalation until the introduction of the Alexandrian calendar by Augustus in the 20s BC, causing it to slowly move through the Sothic cycle against the solar, Sothic, and Julian years. [6] [3] [64] Dates were typically given in a YMD format. [55]

The civil calendar was apparently preceded by an observational lunar calendar which was eventually made lunisolar [q] and fixed to the civil calendar, probably in 357 BC. [67] The months of these calendars were known as "temple months" [68] and used for liturgical purposes until the closing of Egypt's pagan temples under Theodosius I [69] in the AD 390s and the subsequent suppression of individual worship by his successors. [70]

Smaller units of time were vague approximations for most of Egyptian history. Hours—known by a variant of the word for "stars" [71]—were initially only demarcated at night and varied in length. They were measured using decan stars and by water clocks. Equal 24-part divisions of the day were only introduced in 127 BC. Division of these hours into 60 equal minutes is attested in Ptolemy's 2nd-century works.

Units of Time [6] [2]
Name Days
English Egyptian
hour
E34
N35
W24
X1
N14
N5
[r]
wnwt variable
day
S29S29S29Z7N5
[s]
sw 1
decan
decade
week
S29S29S29Z7N5V20
[t]
"ten-day"
sw mḏ [81]
10
month
N11
N14
D46
N5
[u]
ꜣbd 30
season
M17X1
D21
G43M6
ı͗trw [v] 120
year
M4X1
Z1
[w]
rnpt 365
365+14

See also

Notes

  1. ^ Alternative representations for the Egyptian digit include
    D50Z1
    and
    I10D58D36D50
    . [14]
  2. ^ Alternative representations for the Egyptian palm include
    D46
    ,
    N11
    ,
    O42
    and
    O42Q3
    N11
    . [14]
  3. ^ Alternative representations for the Egyptian hand include
    D46
    X1 F51
    ,
    D46
    X1 Z1
    , and
    U28X1
    D47
    . [14]
  4. ^ Alternative representations for the Egyptian fist include
    Aa1
    I9
    D36
    D49
    and
    Aa1
    I9
    D36D49
    Z1
    as ḫf and
    G1G17G17D49
    ,
    G1G17G17X1
    D49
    , and
    M17G17D49
    as ꜣmm. [14]
  5. ^ Alternative representations for the Egyptian double handbreadth include
    D48D48
    . [14]
  6. ^ Alternative representations for the Egyptian half-cubit include
    Z12
    of uncertain pronunciation. [14]
  7. ^ Alternative representations of the Egyptian cubit or royal cubit include
    D36
    ,
    D36
    Y1
    ,
    D36
    Z1
    ,
    V22
    D36
    ,
    V22
    D42
    ,
    V22
    Z1
    D36
    , [14] all pronounced m , [14] and the explicit "royal" or "sacred cubit"
    M23t
    n
    D42
    , [13] pronounced m nswt [14] or n -swt. [18]
  8. ^ Alternative representations of the Egyptian rod include
    M3
    [30] and
    M3
    X1 Z1
    N35N35
    U19
    W24G43V28V1
    ,
    M3
    X1 Z1
    N35N35
    U19
    W24
    V28V1
    , and
    M3
    X1 Z1
    N35U19W24V28
    , [14] which were pronounced ḫt n nw [11] ( Coptic: ϣⲉ ⲛ ⲛⲟϩ, she n noh). [22]
  9. ^ Alternative representations of the Egyptian schoenus include
    M17X1
    D21
    G43D54
    ,
    M17X1
    D21
    G43D54Z1
    ,
    M17X1
    D21
    G43N36
    ,
    M17X1
    D21
    N35AD54
    N21 Z1
    ,
    M17X1 Z7
    D21
    N35AD54
    ,
    M17X1 Z7
    D21
    N35AN17
    N21 N21
    Z2
    ,
    M17X1 Z7
    D21
    N35AN36
    N21 Z1
    Z2
    ,
    M17X1 Z7
    D21
    N35AN36
    N23
    ,
    M17X1
    D21
    Z7N37
    Z2
    , and
    M17D21D56D54
    . [14]
  10. ^ The Egyptian reed was written
    N35
    D58 M17
    M3
    or
    N35
    D58
    M17Z7T19
    and pronounced nb . [14]
  11. ^ Alternative representations of the 100-square-cubit measure include
    D41
    and
    D41
    N16
    , both pronounced m t , [14] and
    V28G1X1N37M12
    .[ citation needed]
  12. ^ Alternative representations of the setat include
    N18
    ,
    O39
    Z1
    ,
    S22
    X1 X1
    ,
    S29V13
    V2
    X1
    O39
    ,
    V2
    X1 N23
    ,
    V2
    X1 X1
    N23
    Z1
    ,
    V2
    X1 X1
    O39
    ,
    V2
    X1 Z4
    ,
    V2
    X1 Z4
    N23Z1
    Z1
    , and
    D35
    X1 Z4
    V20
    Z2
    , all pronounced s ꜣt. [14]
  13. ^ Alternative representations of the 18 setat include
    Z30
    . [14]
  14. ^ Alternative representations of the quarter-setat include
    Aa2
    Y1
    .[ citation needed]
  15. ^ Alternative representations of the half-setat include
    W11S29Aa13
    , pronounced gs,
    D41
    , pronounced rmn, [14] and
    Y5
    N35
    M40
    .[ citation needed]
  16. ^ Alternative representations of the thousand-ta measure include
    M12N16
    N23 Z1
    ,
    M12N17
    , and
    M12Z1N35N16
    N23 Z1
    . [14]
  17. ^ Parker extensively developed the thesis that the predynastic lunar calendar was already lunisolar, using intercalary months every 2 or 3 years to maintain Sirius's return to the night sky in its twelfth month, [65] but no evidence of such intercalation exists predating the schematic lunisolar calendar developed in 4th century BC. [66]
  18. ^ Variant representations of hour include
    E34
    N35
    D54
    , [72]
    E34
    N35
    W24
    X1
    N5
    ,
    E34
    N35
    W24 X1
    N14
    ,
    E34
    N35
    W24G43X1
    N14
    N5
    Z1
    , [73]
    E34
    N35
    W24
    X1
    N14X1
    N5
    Z1
    ,
    E34
    N35
    W24
    X1
    N2N5Z1
    ,
    E34
    N35
    W24
    X1
    N2D6
    (properly
    N46B
    with a star at the end of the line and a second shorter line to its right), [71]
    E34
    N35
    W24
    Z7
    N14N5
    Z2
    , [74]
    N5
    Z2
    , [75]
    N14
    V13
    N5
    ,
    N14
    V13
    N5
    Z2
    ,
    N14
    X1 N5
    ,
    N14
    X1
    N5
    Z2
    , [76]
    N14
    X1 Z1
    , [77]
    T14X1
    N5
    , [78] and
    E34N35W24X1N14
    .[ citation needed] As nwt, hour also appears as
    N35
    U19
    W24G43X1
    N5
    . [79]
  19. ^ Variant representations of day include
    N5
    , [80]
    S29S29S29G43N5
    , [81] and
    S29S29Z4N5
    . [82] In the plural sww, it appears as
    O35G43N5
    Z2
    [83]
    S29G43N5
    Z2
    [84] and
    S29S29S29N5
    . [81] As hrw ("daytime", "day"), it appears as
    N5Z1
    , [80]
    O4N5
    , [85]
    Z5
    N5
    Z1
    , [86]
    O1
    D21
    N5Z1
    , [87]
    O4G1D21
    N5 Z1
    , [88]
    O4G1D21
    Z7
    N5Z1
    , [89]
    O4G1Z7N5
    Z1
    , [90]
    O4G43N5
    Z1
    , [91]
    O4Z1G43N5
    ,
    O4Z5N5Z1
    , [92]
    O4Z5X1
    N5
    ,
    O4Z5Z5N5
    ,
    O4Z5Z5Z1
    , [93] and
    O4
    D21
    G43N5
    Z1
    . [94] As rꜥ ("sun", "day"), it appears as
    N5
    ,
    N5Z1
    , [80] and
    D21
    D36
    N5Z1
    . [95] As ḏt, day appears as
    I10
    X1 Z1
    D12
    , although properly the loaf and stroke are smaller and fit within the curve of the snake. [96]
  20. ^ Variant representations of decan include
    S29S29Z7N5V20
    . [82]
  21. ^ Variant representations of month include
    N11
    ,
    N11
    N14
    ,
    N11
    N14
    D46
    , [97]
    N11
    N14
    D46
    ,[ citation needed]
    N11
    N14
    D46
    N5 Z1
    ,
    N11
    N14 D46
    Z7N5
    ,
    N11
    N14 Z1
    D46
    N5 Z1
    , and
    N11
    N14 Z5 Z5
    N5
    . [98] In the plural ꜣbdtyw, it appears as
    N11
    N14 D46
    G4Z7
    Z7
    X1
    N5
    . [97] As ꜣbdw, month appears as
    G1N11
    D46
    G43
    . [99]
  22. ^ In the plural ı͗trw, "seasons" appears as
    M17V13
    D21
    G43M5
    (properly
    M5B
    with a triangular leaf), [100]
    M17X1
    D21
    G43M4M4M4N5 N5
    N5
    , and
    M17X1
    D21
    E23M5M5M5
    , although properly the palm branches of the last are reversed. [101] As tr ("time", "period", "season"), it appears as
    M6N5
    , [102]
    M17X1
    D21
    N5
    , [103]
    X1
    D21
    M6N5
    , [104] and
    X1
    D21
    M17M6N5
    . [105] In the dual number, this appears as trwy in
    X1
    D21
    G43M6N5
    N5
    ,
    X1
    D21
    M6N5
    N5
    , [104] and
    X1
    D21
    M17M6Z4G43N5
    N5
    . [105] In the plural, this appears as trw in
    M17G43X1
    D21
    G43M6N5
    Z2
    , [106]
    M17X1
    D21
    M6N5
    Z2
    , [103] and
    X1
    D21
    G43M4N5
    Z2
    . [104]
  23. ^ Variant representations of year include
    M5
    ,
    M7X1
    Z1
    , [102]
    M4X1
    and
    M4X1
    Z1
    G7
    . [107] In the plural rnpwt, it appears as
    D21
    N35
    Q3 Z2
    on the Naucratis Stela [108] and as
    M4M4M4
    ,
    M4M4M4X1
    Z1
    Y1
    Z2
    ,
    M4M4M4X1
    Z2
    ,
    M4X1
    Z1
    Z3A
    ,
    M4X1
    Z2
    , [107] and
    M4Z3
    . [102]

References

Citations

  1. ^ Clagett 1999, p. 3.
  2. ^ a b c d e f g h Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2007
  3. ^ a b c d Englebach, Clarke (1990). Ancient Egyptian Construction and Architecture. New York: Dover. ISBN  0486264858.
  4. ^ Lepsius (1865), pp. 57 ff.
  5. ^ a b Loprieno, Antonio (1996). Ancient Egyptian. New York: CUP. ISBN  0521448492.
  6. ^ a b c d e f g h i Clagett (1999).
  7. ^ Gardiner, Allen (1994). Egyptian Grammar 3rd Edition. Oxford: Griffith Institute. ISBN  0900416351.
  8. ^ a b Faulkner, Raymond (1991). A Concise Dictionary of Middle Egyptian. Griffith Institute Asmolean Museum, Oxford. ISBN  0900416327.
  9. ^ a b c d e Gillings, Richard (1972). Mathematics in the Time of the Pharaohs. MIT. ISBN  0262070456.
  10. ^ Gardiner, §266, pp. 199–200. [3] [8] [9]
  11. ^ a b c d e f g h i j k Clagett (1999), p.  7.
  12. ^ a b c Clagett (1999), p.  9.
  13. ^ a b c Lepsius (1865), p.  43.
  14. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z Vygus, Mark (2015), Middle Egyptian Dictionary (PDF).
  15. ^ Crum (1939), p. 597.
  16. ^ a b c Journal of Egyptian Archaeology, Vol. IV, Egypt Exploration Fund, 1917, p. 135.
  17. ^ a b c d e f g Bagnall (2009), p.  186.
  18. ^ a b c d e f g h i j k l m n o p q r s t Clagett (1999), p.  8.
  19. ^ a b c d Crum (1939), p. 574.
  20. ^ a b c d e f g h i j k Dollinger, André (2012), "Counting and Measuring", Pharaonic Egypt, Reshafim{{ citation}}: CS1 maint: location missing publisher ( link).
  21. ^ Crum (1939), p. 742.
  22. ^ a b c d e f g Feder, Frank; et al., Online Coptic Dictionary, Washington: Georgetown.
  23. ^ a b Crum (1939), p. 842.
  24. ^ Crum (1939), p. 305.
  25. ^ Crum (1939), p. 58.
  26. ^ a b Crum (1939), p. 210.
  27. ^ Crum (1939), p. 211.
  28. ^ Obenga, Théophile (2004), African Philosophy: The Pharaonic Period 2780–330 BC, Per Ankh, p. 460.
  29. ^ a b c Bagnall (2009), p.  185.
  30. ^ Abd el-Mohsen Bakir (1978), Hat-'a em Sbayet r-en Kemet: An Introduction to the Study of the Egyptian Language: A Semitic Approach, General Egyptian Book Organization, p. 70.
  31. ^ a b Crum (1939), p. 722.
  32. ^ a b Crum (1939), p. 611.
  33. ^ Lepsius (1865), p.  44.
  34. ^ Ridgeway, William (1890), "Mensura", A Dictionary of Greek and Roman Antiquities, London: John Murray.
  35. ^ Transactions and Proceedings, American Philological Association, 1941, p. 443.
  36. ^ Janssen, Jozef M.A. (1956), "3997: Iversen, Erik, Canon and Proportions in Egyptian Art", Annual Egyptological Bibliography 1955, Leiden: E.J. Brill for the International Association of Egyptologists, p.  1313.
  37. ^ Digital Egypt: Measuring area in Ancient Egypt
  38. ^ a b c d e f g h Clagett (1999), p.  12.
  39. ^ a b c d Clagett (1999), p.  13.
  40. ^ Crum (1939), p. 790.
  41. ^ Crum (1939), p. 360.
  42. ^ Crum (1939), p. 367.
  43. ^ Crum (1939), p. 570.
  44. ^ Pommerening, T. (2003), "Altagyptische Rezepturen Netrologisch Neu Onterpretiert", Berichte zur Wissenschaftgeschichte, No. 26, p. 1–16. (in German)
  45. ^ a b c "Measuring Volume in Ancient Egypt", Digital Egypt for Universities, London: University College, 2002.
  46. ^ Allen, James P. (2014), Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphics, 3rd ed., Cambridge: Cambridge University Press, p.  129, ISBN  9781139917094.
  47. ^ a b Katz, Victor J.; et al., eds. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press, p. 17, ISBN  978-0-691-11485-9.
  48. ^ "Weights and Measures", Encyclopaedia Britannica, 9th ed., vol. XXIV, 1888.
  49. ^ Weigall (1908), p. ix.
  50. ^ Weigall (1908), pp. iii & ix.
  51. ^ Tetley (2014), p.  39.
  52. ^ Winlock (1940), p. 453.
  53. ^ Clagett (1995), p.  4–5.
  54. ^ Clagett (1995), p.  28.
  55. ^ a b Clagett (1995), p.  5.
  56. ^ Parker (1950), p. 23.
  57. ^ Parker (1950), p. 7.
  58. ^ Spalinger (1995), p. 33.
  59. ^ Spalinger (1995), p. 35.
  60. ^ Parker (1950), pp. 43–5.
  61. ^ Clagett (1995), p. 14–15.
  62. ^ Clagett (1995), p.  4.
  63. ^ Jauhiainen (2009), p. 39.
  64. ^ Marshall Clagett, Ancient Egyptian Science: Calendars, clocks, and astronomy, 1989
  65. ^ Parker (1950), pp. 30–2.
  66. ^ Tetley (2014), p.  153.
  67. ^ Clagett (1995), p.  26.
  68. ^ Parker (1950), p. 17.
  69. ^ Theodosian Code 16.10.12
  70. ^ Høyrup, p. 13.
  71. ^ a b Vygus (2015), p. 409.
  72. ^ Vygus (2015), p. 399.
  73. ^ Vygus (2015), p. 408.
  74. ^ Vygus (2015), p. 410.
  75. ^ Vygus (2015), p. 1229.
  76. ^ Vygus (2015), p. 1239.
  77. ^ Vygus (2015), p. 1240.
  78. ^ Vygus (2015), p. 1984.
  79. ^ Vygus (2015), p. 1382.
  80. ^ a b c Vygus (2015), p. 1228.
  81. ^ a b c Vygus (2015), p. 1880.
  82. ^ a b Vygus (2015), p. 1881.
  83. ^ Vygus (2015), p. 1611.
  84. ^ Vygus (2015), p. 1790.
  85. ^ Vygus (2015), p. 1500.
  86. ^ Vygus (2015), p. 2467.
  87. ^ Vygus (2015), p. 1461.
  88. ^ Vygus (2015), p. 1477.
  89. ^ Vygus (2015), p. 1478.
  90. ^ Vygus (2015), p. 1492.
  91. ^ Vygus (2015), p. 1495.
  92. ^ Vygus (2015), p. 1513.
  93. ^ Vygus (2015), p. 1514.
  94. ^ Vygus (2015), p. 1471.
  95. ^ Vygus (2015), p. 75.
  96. ^ Vygus (2015), p. 822.
  97. ^ a b Vygus (2015), p. 1233.
  98. ^ Vygus (2015), p. 1234.
  99. ^ Vygus (2015), p. 547.
  100. ^ Vygus (2015), p. 1156.
  101. ^ Vygus (2015), p. 1168.
  102. ^ a b c Vygus (2015), p. 958.
  103. ^ a b Vygus (2015), p. 1167.
  104. ^ a b c Vygus (2015), p. 2386.
  105. ^ a b Vygus (2015), p. 2387.
  106. ^ Vygus (2015), p. 1085.
  107. ^ a b Vygus (2015), p. 957.
  108. ^ Vygus (2015), p. 103.

Bibliography

External links

From Wikipedia, the free encyclopedia

The ancient Egyptian units of measurement are those used by the dynasties of ancient Egypt prior to its incorporation in the Roman Empire and general adoption of Roman, Greek, and Byzantine units of measurement. The units of length seem to have originally been anthropic, based on various parts of the human body, although these were standardized using cubit rods, strands of rope, and official measures maintained at some temples.

Following Alexander the Great's conquest of Persia and subsequent death, his bodyguard and successor Ptolemy assumed control in Egypt, partially reforming its measurements, introducing some new units and hellenized names for others.

Length

Egyptian units of length are attested from the Early Dynastic Period. Although it dates to the 5th dynasty, the Palermo stone recorded the level of the Nile River during the reign of the Early Dynastic pharaoh Djer, when the height of the Nile was recorded as 6 cubits and 1 palm [1] (about 3.217 m or 10 ft 6.7 in). A Third Dynasty diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon depicting this diagram was found near the Step Pyramid of Saqqara. A curve is divided into five sections and the height of the curve is given in cubits, palms, and digits in each of the sections. [2] [3]

At some point, lengths were standardized by cubit rods. Examples have been found in the tombs of officials, noting lengths up to remen. Royal cubits were used for land measures such as roads and fields. Fourteen rods, including one double-cubit rod, were described and compared by Lepsius. [4] Two examples are known from the Saqqara tomb of Maya, the treasurer of Tutankhamun. Another was found in the tomb of Kha ( TT8) in Thebes. These cubits are about 52.5 cm (20.7 in) long and are divided into palms and hands: each palm is divided into four fingers from left to right and the fingers are further subdivided into ro from right to left. The rules are also divided into hands [5] so that for example one foot is given as three hands and fifteen fingers and also as four palms and sixteen fingers. [6] [3] [7] [8] [9] [5]

Cubit rod from the Turin Museum.

Surveying and itinerant measurement were undertaken using rods, poles, and knotted cords of rope. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots tied at regular intervals. Similar scenes can be found in the tombs of Amenhotep-Sesi, Khaemhat and Djeserkareseneb. The balls of rope are also shown in New Kingdom statues of officials such as Senenmut, Amenemhet-Surer, and Penanhor. [2]

Units of Length [6] [2]
Names Equivalents
English Egyptian Coptic Palms Digits Metric [10]
Digit [11]
Finger [12]
Fingerbreadth [11]
Tebā [13]
D50
[a]
ḏb ⲧⲏⲏⲃⲉ [15] [16] tēēbe 14 1 1.875 cm
Palm [11]
Hand [17]
Shesep [18]
D48
[b]
šsp ϣⲟⲡ [19] [16]
ϣⲟⲟⲡ [19]
ϣⲱⲡ [19]
ϣⲁⲡ [19]
shop
shoop
shōp
shap
1 4 7.5 cm
Hand [20]
Handsbreadth [18]
D46
[c]
ḏrt ϩⲱϩϥ [21] [22] hōhf 1+14 5 9.38 cm
Fist [18]
D49
[d]
ḫf [18]
ꜣmm [14]
ϭⲁϫⲙⲏ [23]
ϫⲁⲙⲏ [23]
qajmē
jamē
1+12 6 11.25 cm
Double Handbreadth [14]
D48
D48
[e]
šspwy 2 8 15 cm [14]
Small Span [18]
Pedj-Sheser
Shat Nedjes [18]
Little Shat [12]
H7G37
p šsr
š ꜣt n ḏs [18]
ⲣⲧⲱ [24] [22]
ⲉⲣⲧⲱ [25]
rtō
ertō
3 12 22.5 cm
Great Span [18]
Half-Cubit [14]
Pedj-Aa
Shat Aa [18]
Great Shat [12]
H7O29
[f]
pḏ [18] [14]
š ꜣt [18]
3+12 14 26 cm
Foot
Djeser [18]
Ser [13]
Bent Arm [18]
D45
ḏsr 4 16 30 cm
Shoulder
Remen [18]
Upper Arm [18]
D41
rmn 5 20 37.5 cm
Small Cubit [20]
Short Cubit [18]
Meh Nedjes [18]
D42G37
m n ḏs
m šsr
ⲙⲁϩⲉ [26] [16]
ⲙⲉϩⲓ [27]
mahe
mehi
6 24 45 cm
Cubit
Royal Cubit [18]
Sacred Cubit [17]
Meh Nesut [11]
Meh Nisut [18]
Mahi
Ell [26]
D42
[g]
m 7 28 52.3 cm [11]
52.5 cm [17]
Pole
Nebiu [28]
N35
D58
M17V1T19
nbiw 8 32 60 cm
Rod
Rod of Cord
Stick of Rope [20]
Khet [11]
Schoinion [29]
W24G43V28
[h]
ḫt ϩⲱⲧⲉ [31]
ϩⲱϯ [31]
hōte
hōti
100 cubits [11] 52.5 m [29]
Schoenus [14]
River-Measure
League [14]
Ater [11]
Iter [20] or Iteru [14]
M17X1
D21
G43N35BN36
N21 Z1
[i]
i͗trw ϣϥⲱ [32]
ϣⲃⲱ [32]
shfō
shvō
20,000 cubits [11] 10.5 km [11]

The digit was also subdivided into smaller fractions of 12, 13, 14, and 116. [33] Minor units include the Middle Kingdom reed of 2 royal cubits, [j] the Ptolemaic xylon ( Greek: ξύλον, lit. "timber") of three royal cubits, [34] [35] the Ptolemaic fathom ( Greek: ὀργυιά, orgyiá; Ancient Egyptian: ḥpt; Coptic: ϩⲡⲟⲧ, hpot) of four lesser cubits, [36] and the kalamos of six royal cubits. [17]

Area

Records of land area also date to the Early Dynastic Period. The Palermo stone records grants of land expressed in terms of kha and setat. Mathematical papyri also include units of land area in their problems. For example, several problems in the Moscow Mathematical Papyrus give the area of rectangular plots of land in terms of setat and the ratio of the sides and then require the scribe to solve for their exact lengths. [6]

The setat was the basic unit of land measure and may originally have varied in size across Egypt's nomes. [20] Later, it was equal to one square khet, where a khet measured 100 cubits. The setat could be divided into strips one khet long and ten cubit wide (a kha). [2] [6] [37]

During the Old Kingdom:

Units of Area
Names Equivalents [38]
English Egyptian Coptic Setat Square
Cubits
Metric
Sa [20]
Eighth
G39
z 1800 12+12 3.4456 m2
Heseb
Fourth
Account Unit [20]
Z9
ḥsb 1400 25 6.8913 m2
Remen
Half
Shoulder [20]
D41
rmn 1200 50 13.783 m2
Ta
Khet [38]
Cubit [39]
Cubit of Land [39]
Land Cubit [14]
Ground Cubit [39]
Cubit Strip [39]
Land Unit [20]
N17
[k]
t
ḫt
m
m itn
ϫⲓⲥⲉ [40] [22] jise 1100 100 [38] 27.565 m2
Kha
Thousand [20]
M12
110 1,000 275.65 m2
Setat [38]
Setjat [38]
Aroura [38]
Square Khet [38]
stF29t
Z4
[l]
s [29]
s ꜣt [38]
ⲥⲱⲧ [41] [22]
ⲥⲧⲉⲓⲱϩⲉ [42] [22]
sōt
steiōhe
1 10,000 2,756.5 m2

During the Middle and New Kingdom, the "eighth", "fourth", "half", and "thousand" units were taken to refer to the setat rather than the cubit strip:

Sa
Eighth
G39
[m]
s 18 1,250 345 m2
Heseb
Fourth
Z9
[n]
hsb
r-fdw
14 2,500 689 m2
Gs
Remen
Half
Aa13
[o]
gs ⲣⲉⲣⲙⲏ [22] rermē 12 5,000 1378 m2
Kha
Thousand
M12
[p]

t
10 100,000 2.76 ha

During the Ptolemaic period, the cubit strip square was surveyed using a length of 96 cubits rather than 100, although the aroura was still figured to compose 2,756.25 m2. [17] A 36 square cubit area was known as a kalamos and a 144 square cubit area as a hamma. [17] The uncommon bikos may have been 1+12 hammata or another name for the cubit strip. [17] The Coptic shipa (ϣⲓⲡⲁ) was a land unit of uncertain value, possibly derived from Nubia. [43]

Volume

A bronze capacity measure inscribed with the cartouches of the birth and throne names of Amenhotep III of the 18th Dynasty

Units of volume appear in the mathematical papyri. For example, computing the volume of a circular granary in RMP 42 involves cubic cubits, khar, heqats, and quadruple heqats. [6] [9] RMP 80 divides heqats of grain into smaller henu.

Problem 80 on the Rhind Mathematical Papyrus: As for vessels (debeh) used in measuring grain by the functionaries of the granary: done into henu, 1 hekat makes 10; 12 makes 5; 14 makes 2+12; etc. [6] [9]
Units of Volume [6] [2]
Names Equivalents
English Egyptian Heqats Ro Metric
Ro
r
r 1320 1 0.015 L
Dja dja 116 20 [44] 0.30 L
Jar
Hinu
hn
W24 V1
W22
hnw 110 32 0.48 L
Barrel
Heqat
Hekat
U9
hqt 1 320 4.8 L
Double Barrel
Double Heqat
Double Hekat
hqty 2 640 9.6 L
Quadruple Heqat ( MK) [45]
Oipe [46] ( NK) [45]
T14U9

ip
t
U9
hqt-fdw
jpt [20]
ipt [45]
4 1,280 19.2 L
Sack
Khar
Aa1
r
khar 20 ( MK)
16 ( NK) [47]
6,400 ( MK)
5120 ( NK)
96.5 L ( MK)
76.8 L ( NK) [47]
Deny
Cubic cubit
deny 30 9,600 144 L

The oipe was also formerly romanized as the apet. [48]

Weight

Green glazed faience weight discovered at Abydos, inscribed for the high steward Aabeni during the late Middle Kingdom
Serpentine weight of 10 daric, inscribed for Taharqa during the 25th Dynasty

Weights were measured in terms of deben. This unit would have been equivalent to 13.6 grams in the Old Kingdom and Middle Kingdom. During the New Kingdom however it was equivalent to 91 grams. For smaller amounts the qedet (110 of a deben) and the shematy (112 of a deben) were used. [2] [9]

Units of Weight [2]
Names Equivalents
English Egyptian Debens Metric
Piece
Shematy
shȝts 112
Qedet
Kedet
Kite
Aa28X1
S106
qdt 110
Deben
D46D58N35
F46
dbn 1 13.6 g ( OK & MK)
91 g ( NK)

The qedet or kedet is also often known as the kite, from the Coptic form of the same name (ⲕⲓⲧⲉ or ⲕⲓϯ). [49] In 19th-century sources, the deben and qedet are often mistakenly transliterated as the uten and kat respectively, although this was corrected by the 20th century. [50]

Time

The former annual flooding of the Nile organized prehistoric and ancient Egypt into three seasons: Akhet ("Flood"), Peret ("Growth"), and Shemu or Shomu ("Low Water" or "Harvest"). [51] [52] [53]

The Egyptian civil calendar in place by Dynasty V [54] followed regnal eras resetting with the ascension of each new pharaoh. [55] It was based on the solar year and apparently initiated during a heliacal rising of Sirius following a recognition of its rough correlation with the onset of the Nile flood. [56] It followed none of these consistently, however. Its year was divided into 3 seasons, 12 months, 36 decans, or 360 days with another 5 epagomenal days [57]—celebrated as the birthdays of five major gods [58] but feared for their ill luck [59]—added "upon the year". The Egyptian months were originally simply numbered within each season [60] but, in later sources, they acquired names from the year's major festivals [61] and the three decans of each one were distinguished as "first", "middle", and "last". [62] It has been suggested that during the Nineteenth Dynasty and the Twentieth Dynasty the last two days of each decan were usually treated as a kind of weekend for the royal craftsmen, with royal artisans free from work. [63] This scheme lacked any provision for leap year intercalation until the introduction of the Alexandrian calendar by Augustus in the 20s BC, causing it to slowly move through the Sothic cycle against the solar, Sothic, and Julian years. [6] [3] [64] Dates were typically given in a YMD format. [55]

The civil calendar was apparently preceded by an observational lunar calendar which was eventually made lunisolar [q] and fixed to the civil calendar, probably in 357 BC. [67] The months of these calendars were known as "temple months" [68] and used for liturgical purposes until the closing of Egypt's pagan temples under Theodosius I [69] in the AD 390s and the subsequent suppression of individual worship by his successors. [70]

Smaller units of time were vague approximations for most of Egyptian history. Hours—known by a variant of the word for "stars" [71]—were initially only demarcated at night and varied in length. They were measured using decan stars and by water clocks. Equal 24-part divisions of the day were only introduced in 127 BC. Division of these hours into 60 equal minutes is attested in Ptolemy's 2nd-century works.

Units of Time [6] [2]
Name Days
English Egyptian
hour
E34
N35
W24
X1
N14
N5
[r]
wnwt variable
day
S29S29S29Z7N5
[s]
sw 1
decan
decade
week
S29S29S29Z7N5V20
[t]
"ten-day"
sw mḏ [81]
10
month
N11
N14
D46
N5
[u]
ꜣbd 30
season
M17X1
D21
G43M6
ı͗trw [v] 120
year
M4X1
Z1
[w]
rnpt 365
365+14

See also

Notes

  1. ^ Alternative representations for the Egyptian digit include
    D50Z1
    and
    I10D58D36D50
    . [14]
  2. ^ Alternative representations for the Egyptian palm include
    D46
    ,
    N11
    ,
    O42
    and
    O42Q3
    N11
    . [14]
  3. ^ Alternative representations for the Egyptian hand include
    D46
    X1 F51
    ,
    D46
    X1 Z1
    , and
    U28X1
    D47
    . [14]
  4. ^ Alternative representations for the Egyptian fist include
    Aa1
    I9
    D36
    D49
    and
    Aa1
    I9
    D36D49
    Z1
    as ḫf and
    G1G17G17D49
    ,
    G1G17G17X1
    D49
    , and
    M17G17D49
    as ꜣmm. [14]
  5. ^ Alternative representations for the Egyptian double handbreadth include
    D48D48
    . [14]
  6. ^ Alternative representations for the Egyptian half-cubit include
    Z12
    of uncertain pronunciation. [14]
  7. ^ Alternative representations of the Egyptian cubit or royal cubit include
    D36
    ,
    D36
    Y1
    ,
    D36
    Z1
    ,
    V22
    D36
    ,
    V22
    D42
    ,
    V22
    Z1
    D36
    , [14] all pronounced m , [14] and the explicit "royal" or "sacred cubit"
    M23t
    n
    D42
    , [13] pronounced m nswt [14] or n -swt. [18]
  8. ^ Alternative representations of the Egyptian rod include
    M3
    [30] and
    M3
    X1 Z1
    N35N35
    U19
    W24G43V28V1
    ,
    M3
    X1 Z1
    N35N35
    U19
    W24
    V28V1
    , and
    M3
    X1 Z1
    N35U19W24V28
    , [14] which were pronounced ḫt n nw [11] ( Coptic: ϣⲉ ⲛ ⲛⲟϩ, she n noh). [22]
  9. ^ Alternative representations of the Egyptian schoenus include
    M17X1
    D21
    G43D54
    ,
    M17X1
    D21
    G43D54Z1
    ,
    M17X1
    D21
    G43N36
    ,
    M17X1
    D21
    N35AD54
    N21 Z1
    ,
    M17X1 Z7
    D21
    N35AD54
    ,
    M17X1 Z7
    D21
    N35AN17
    N21 N21
    Z2
    ,
    M17X1 Z7
    D21
    N35AN36
    N21 Z1
    Z2
    ,
    M17X1 Z7
    D21
    N35AN36
    N23
    ,
    M17X1
    D21
    Z7N37
    Z2
    , and
    M17D21D56D54
    . [14]
  10. ^ The Egyptian reed was written
    N35
    D58 M17
    M3
    or
    N35
    D58
    M17Z7T19
    and pronounced nb . [14]
  11. ^ Alternative representations of the 100-square-cubit measure include
    D41
    and
    D41
    N16
    , both pronounced m t , [14] and
    V28G1X1N37M12
    .[ citation needed]
  12. ^ Alternative representations of the setat include
    N18
    ,
    O39
    Z1
    ,
    S22
    X1 X1
    ,
    S29V13
    V2
    X1
    O39
    ,
    V2
    X1 N23
    ,
    V2
    X1 X1
    N23
    Z1
    ,
    V2
    X1 X1
    O39
    ,
    V2
    X1 Z4
    ,
    V2
    X1 Z4
    N23Z1
    Z1
    , and
    D35
    X1 Z4
    V20
    Z2
    , all pronounced s ꜣt. [14]
  13. ^ Alternative representations of the 18 setat include
    Z30
    . [14]
  14. ^ Alternative representations of the quarter-setat include
    Aa2
    Y1
    .[ citation needed]
  15. ^ Alternative representations of the half-setat include
    W11S29Aa13
    , pronounced gs,
    D41
    , pronounced rmn, [14] and
    Y5
    N35
    M40
    .[ citation needed]
  16. ^ Alternative representations of the thousand-ta measure include
    M12N16
    N23 Z1
    ,
    M12N17
    , and
    M12Z1N35N16
    N23 Z1
    . [14]
  17. ^ Parker extensively developed the thesis that the predynastic lunar calendar was already lunisolar, using intercalary months every 2 or 3 years to maintain Sirius's return to the night sky in its twelfth month, [65] but no evidence of such intercalation exists predating the schematic lunisolar calendar developed in 4th century BC. [66]
  18. ^ Variant representations of hour include
    E34
    N35
    D54
    , [72]
    E34
    N35
    W24
    X1
    N5
    ,
    E34
    N35
    W24 X1
    N14
    ,
    E34
    N35
    W24G43X1
    N14
    N5
    Z1
    , [73]
    E34
    N35
    W24
    X1
    N14X1
    N5
    Z1
    ,
    E34
    N35
    W24
    X1
    N2N5Z1
    ,
    E34
    N35
    W24
    X1
    N2D6
    (properly
    N46B
    with a star at the end of the line and a second shorter line to its right), [71]
    E34
    N35
    W24
    Z7
    N14N5
    Z2
    , [74]
    N5
    Z2
    , [75]
    N14
    V13
    N5
    ,
    N14
    V13
    N5
    Z2
    ,
    N14
    X1 N5
    ,
    N14
    X1
    N5
    Z2
    , [76]
    N14
    X1 Z1
    , [77]
    T14X1
    N5
    , [78] and
    E34N35W24X1N14
    .[ citation needed] As nwt, hour also appears as
    N35
    U19
    W24G43X1
    N5
    . [79]
  19. ^ Variant representations of day include
    N5
    , [80]
    S29S29S29G43N5
    , [81] and
    S29S29Z4N5
    . [82] In the plural sww, it appears as
    O35G43N5
    Z2
    [83]
    S29G43N5
    Z2
    [84] and
    S29S29S29N5
    . [81] As hrw ("daytime", "day"), it appears as
    N5Z1
    , [80]
    O4N5
    , [85]
    Z5
    N5
    Z1
    , [86]
    O1
    D21
    N5Z1
    , [87]
    O4G1D21
    N5 Z1
    , [88]
    O4G1D21
    Z7
    N5Z1
    , [89]
    O4G1Z7N5
    Z1
    , [90]
    O4G43N5
    Z1
    , [91]
    O4Z1G43N5
    ,
    O4Z5N5Z1
    , [92]
    O4Z5X1
    N5
    ,
    O4Z5Z5N5
    ,
    O4Z5Z5Z1
    , [93] and
    O4
    D21
    G43N5
    Z1
    . [94] As rꜥ ("sun", "day"), it appears as
    N5
    ,
    N5Z1
    , [80] and
    D21
    D36
    N5Z1
    . [95] As ḏt, day appears as
    I10
    X1 Z1
    D12
    , although properly the loaf and stroke are smaller and fit within the curve of the snake. [96]
  20. ^ Variant representations of decan include
    S29S29Z7N5V20
    . [82]
  21. ^ Variant representations of month include
    N11
    ,
    N11
    N14
    ,
    N11
    N14
    D46
    , [97]
    N11
    N14
    D46
    ,[ citation needed]
    N11
    N14
    D46
    N5 Z1
    ,
    N11
    N14 D46
    Z7N5
    ,
    N11
    N14 Z1
    D46
    N5 Z1
    , and
    N11
    N14 Z5 Z5
    N5
    . [98] In the plural ꜣbdtyw, it appears as
    N11
    N14 D46
    G4Z7
    Z7
    X1
    N5
    . [97] As ꜣbdw, month appears as
    G1N11
    D46
    G43
    . [99]
  22. ^ In the plural ı͗trw, "seasons" appears as
    M17V13
    D21
    G43M5
    (properly
    M5B
    with a triangular leaf), [100]
    M17X1
    D21
    G43M4M4M4N5 N5
    N5
    , and
    M17X1
    D21
    E23M5M5M5
    , although properly the palm branches of the last are reversed. [101] As tr ("time", "period", "season"), it appears as
    M6N5
    , [102]
    M17X1
    D21
    N5
    , [103]
    X1
    D21
    M6N5
    , [104] and
    X1
    D21
    M17M6N5
    . [105] In the dual number, this appears as trwy in
    X1
    D21
    G43M6N5
    N5
    ,
    X1
    D21
    M6N5
    N5
    , [104] and
    X1
    D21
    M17M6Z4G43N5
    N5
    . [105] In the plural, this appears as trw in
    M17G43X1
    D21
    G43M6N5
    Z2
    , [106]
    M17X1
    D21
    M6N5
    Z2
    , [103] and
    X1
    D21
    G43M4N5
    Z2
    . [104]
  23. ^ Variant representations of year include
    M5
    ,
    M7X1
    Z1
    , [102]
    M4X1
    and
    M4X1
    Z1
    G7
    . [107] In the plural rnpwt, it appears as
    D21
    N35
    Q3 Z2
    on the Naucratis Stela [108] and as
    M4M4M4
    ,
    M4M4M4X1
    Z1
    Y1
    Z2
    ,
    M4M4M4X1
    Z2
    ,
    M4X1
    Z1
    Z3A
    ,
    M4X1
    Z2
    , [107] and
    M4Z3
    . [102]

References

Citations

  1. ^ Clagett 1999, p. 3.
  2. ^ a b c d e f g h Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2007
  3. ^ a b c d Englebach, Clarke (1990). Ancient Egyptian Construction and Architecture. New York: Dover. ISBN  0486264858.
  4. ^ Lepsius (1865), pp. 57 ff.
  5. ^ a b Loprieno, Antonio (1996). Ancient Egyptian. New York: CUP. ISBN  0521448492.
  6. ^ a b c d e f g h i Clagett (1999).
  7. ^ Gardiner, Allen (1994). Egyptian Grammar 3rd Edition. Oxford: Griffith Institute. ISBN  0900416351.
  8. ^ a b Faulkner, Raymond (1991). A Concise Dictionary of Middle Egyptian. Griffith Institute Asmolean Museum, Oxford. ISBN  0900416327.
  9. ^ a b c d e Gillings, Richard (1972). Mathematics in the Time of the Pharaohs. MIT. ISBN  0262070456.
  10. ^ Gardiner, §266, pp. 199–200. [3] [8] [9]
  11. ^ a b c d e f g h i j k Clagett (1999), p.  7.
  12. ^ a b c Clagett (1999), p.  9.
  13. ^ a b c Lepsius (1865), p.  43.
  14. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z Vygus, Mark (2015), Middle Egyptian Dictionary (PDF).
  15. ^ Crum (1939), p. 597.
  16. ^ a b c Journal of Egyptian Archaeology, Vol. IV, Egypt Exploration Fund, 1917, p. 135.
  17. ^ a b c d e f g Bagnall (2009), p.  186.
  18. ^ a b c d e f g h i j k l m n o p q r s t Clagett (1999), p.  8.
  19. ^ a b c d Crum (1939), p. 574.
  20. ^ a b c d e f g h i j k Dollinger, André (2012), "Counting and Measuring", Pharaonic Egypt, Reshafim{{ citation}}: CS1 maint: location missing publisher ( link).
  21. ^ Crum (1939), p. 742.
  22. ^ a b c d e f g Feder, Frank; et al., Online Coptic Dictionary, Washington: Georgetown.
  23. ^ a b Crum (1939), p. 842.
  24. ^ Crum (1939), p. 305.
  25. ^ Crum (1939), p. 58.
  26. ^ a b Crum (1939), p. 210.
  27. ^ Crum (1939), p. 211.
  28. ^ Obenga, Théophile (2004), African Philosophy: The Pharaonic Period 2780–330 BC, Per Ankh, p. 460.
  29. ^ a b c Bagnall (2009), p.  185.
  30. ^ Abd el-Mohsen Bakir (1978), Hat-'a em Sbayet r-en Kemet: An Introduction to the Study of the Egyptian Language: A Semitic Approach, General Egyptian Book Organization, p. 70.
  31. ^ a b Crum (1939), p. 722.
  32. ^ a b Crum (1939), p. 611.
  33. ^ Lepsius (1865), p.  44.
  34. ^ Ridgeway, William (1890), "Mensura", A Dictionary of Greek and Roman Antiquities, London: John Murray.
  35. ^ Transactions and Proceedings, American Philological Association, 1941, p. 443.
  36. ^ Janssen, Jozef M.A. (1956), "3997: Iversen, Erik, Canon and Proportions in Egyptian Art", Annual Egyptological Bibliography 1955, Leiden: E.J. Brill for the International Association of Egyptologists, p.  1313.
  37. ^ Digital Egypt: Measuring area in Ancient Egypt
  38. ^ a b c d e f g h Clagett (1999), p.  12.
  39. ^ a b c d Clagett (1999), p.  13.
  40. ^ Crum (1939), p. 790.
  41. ^ Crum (1939), p. 360.
  42. ^ Crum (1939), p. 367.
  43. ^ Crum (1939), p. 570.
  44. ^ Pommerening, T. (2003), "Altagyptische Rezepturen Netrologisch Neu Onterpretiert", Berichte zur Wissenschaftgeschichte, No. 26, p. 1–16. (in German)
  45. ^ a b c "Measuring Volume in Ancient Egypt", Digital Egypt for Universities, London: University College, 2002.
  46. ^ Allen, James P. (2014), Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphics, 3rd ed., Cambridge: Cambridge University Press, p.  129, ISBN  9781139917094.
  47. ^ a b Katz, Victor J.; et al., eds. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press, p. 17, ISBN  978-0-691-11485-9.
  48. ^ "Weights and Measures", Encyclopaedia Britannica, 9th ed., vol. XXIV, 1888.
  49. ^ Weigall (1908), p. ix.
  50. ^ Weigall (1908), pp. iii & ix.
  51. ^ Tetley (2014), p.  39.
  52. ^ Winlock (1940), p. 453.
  53. ^ Clagett (1995), p.  4–5.
  54. ^ Clagett (1995), p.  28.
  55. ^ a b Clagett (1995), p.  5.
  56. ^ Parker (1950), p. 23.
  57. ^ Parker (1950), p. 7.
  58. ^ Spalinger (1995), p. 33.
  59. ^ Spalinger (1995), p. 35.
  60. ^ Parker (1950), pp. 43–5.
  61. ^ Clagett (1995), p. 14–15.
  62. ^ Clagett (1995), p.  4.
  63. ^ Jauhiainen (2009), p. 39.
  64. ^ Marshall Clagett, Ancient Egyptian Science: Calendars, clocks, and astronomy, 1989
  65. ^ Parker (1950), pp. 30–2.
  66. ^ Tetley (2014), p.  153.
  67. ^ Clagett (1995), p.  26.
  68. ^ Parker (1950), p. 17.
  69. ^ Theodosian Code 16.10.12
  70. ^ Høyrup, p. 13.
  71. ^ a b Vygus (2015), p. 409.
  72. ^ Vygus (2015), p. 399.
  73. ^ Vygus (2015), p. 408.
  74. ^ Vygus (2015), p. 410.
  75. ^ Vygus (2015), p. 1229.
  76. ^ Vygus (2015), p. 1239.
  77. ^ Vygus (2015), p. 1240.
  78. ^ Vygus (2015), p. 1984.
  79. ^ Vygus (2015), p. 1382.
  80. ^ a b c Vygus (2015), p. 1228.
  81. ^ a b c Vygus (2015), p. 1880.
  82. ^ a b Vygus (2015), p. 1881.
  83. ^ Vygus (2015), p. 1611.
  84. ^ Vygus (2015), p. 1790.
  85. ^ Vygus (2015), p. 1500.
  86. ^ Vygus (2015), p. 2467.
  87. ^ Vygus (2015), p. 1461.
  88. ^ Vygus (2015), p. 1477.
  89. ^ Vygus (2015), p. 1478.
  90. ^ Vygus (2015), p. 1492.
  91. ^ Vygus (2015), p. 1495.
  92. ^ Vygus (2015), p. 1513.
  93. ^ Vygus (2015), p. 1514.
  94. ^ Vygus (2015), p. 1471.
  95. ^ Vygus (2015), p. 75.
  96. ^ Vygus (2015), p. 822.
  97. ^ a b Vygus (2015), p. 1233.
  98. ^ Vygus (2015), p. 1234.
  99. ^ Vygus (2015), p. 547.
  100. ^ Vygus (2015), p. 1156.
  101. ^ Vygus (2015), p. 1168.
  102. ^ a b c Vygus (2015), p. 958.
  103. ^ a b Vygus (2015), p. 1167.
  104. ^ a b c Vygus (2015), p. 2386.
  105. ^ a b Vygus (2015), p. 2387.
  106. ^ Vygus (2015), p. 1085.
  107. ^ a b Vygus (2015), p. 957.
  108. ^ Vygus (2015), p. 103.

Bibliography

External links


Videos

Youtube | Vimeo | Bing

Websites

Google | Yahoo | Bing

Encyclopedia

Google | Yahoo | Bing

Facebook